What are the proper uses for the words nonrational and irrational.
Well, in short--without getting into a debate about what constitutes "rational" thinking--the prefx 'non-' means, doesn't exist, whereas the prefix 'ir-' means, opposite. So, for example, an irrational person has the ability to rationalize but can be illogical and/or unreasonable. Humans are not, generally, described as being "non-rational", not having human cognitive skills. A non-rational species is just that. Such a species doesn't have the ability to "rationalize" in the same way as humans do.